What is a GeoPackage file?
GeoPackage is an open OGC standard built on SQLite. One .gpkg file can hold many vector layers, raster tiles and attribute tables together.
It has none of the Shapefile's limits — long field names, large files, proper data types — and it is the default format in QGIS.
What is a Shapefile file?
The Shapefile is Esri's vector format from the early 1990s. One dataset is a set of files — .shp (geometry), .shx (index), .dbf (attributes) and .prj (coordinate system) — usually shared as a .zip.
It is still the most widely supported GIS format, but it has hard limits: one geometry type per file, field names of up to 10 characters and a 2 GB size cap.